Parallel Lines & Transversals

Parallel Lines & Transversals

Parallel Lines

Remember, PARALLEL LINES are lines that lie in the same plane and do not intersect.

Transversal

A TRANSVERSAL is a line that intersects two or more lines at distinct points.

Parallel Lines & Transversals

When a TRANSVERSAL intersects PARALLEL LINES, 8 angles are formed.

These angles have special realtionships that are helpful to remember.

Multiple Choice

Which figure shows a set of parallel lines?

• Figure 1

• Figure 2

• Figure 3

• Figure 4

Multiple Choice

True or False: This figure shows a picture of a transversal.

• True, the transversal goes from the top left to bottom right.

• True, the transversal goes from the top right to bottom left.

• False, this is a picture of intersecting lines.

The 8 angles formed by two parallel lines and a transversal create the following special angle pairs:

• Corresponding Angles

• Vertical Angles

• Consecutive Interior Angles

• Consecutive Exterior Angles

• Alternate Interior Angles

• Alternate Exterior Angles

Corresponding Angles

Just like corresponding parts of similar figures, CORRESPONDING ANGLES are in the same position on each parallel line.

These angle pairs are CONGRUENT.

Vertical Angles

VERTICAL ANGLES are pairs of opposite angles formed by intersecting lines.

These angle pairs are CONGRUENT.

Multiple Choice

What angle corresponds to  $\angle1$  ?

•  $\angle7$ 

• $\angle5$

• $\angle3$

• $\angle2$

Multiple Choice

Which angles are vertical angles?

•  $\angle5\ and\ \angle3$ 

•  $\angle2\ and\ \angle4$ 

•  $\angle1\ and\ \angle4$ 

• $\angle6\ and\ \angle4$

Interior vs. Exterior

Angles in between the parallel lines are called INTERIOR ANGLES.

Angles that are outside of the parallel lines are EXTERIOR ANGLES.

Consecutive vs. Alternate

CONSECUTIVE angles are on the SAME SIDE of the transversal.

ALTERNATE angles are on OPPOSITE SIDES of the transversal.

Consecutive Interior Angles

Angles on the SAME SIDE of the transversal and INSIDE of the parallel lines.

These angles are SUPPLEMENTARY ANGLES.

Consecutive Exterior Angles

Angles on the SAME SIDE of the transversal and OUTSIDE of the parallel lines.

These angles are SUPPLEMENTARY ANGLES.

Alternate Interior Angles

Angles on the OPPOSITE SIDES of the transversal and INSIDE of the parallel lines.

These angles are CONGRUENT.

Alternate Exterior Angles

Angles on the OPPOSITE SIDES of the transversal and OUTSIDE of the parallel lines.

These angles are CONGRUENT.

Multiple Choice

∠3 and ∠6 are...

• Supplementary angles

• Vertical angles

• Corresponding angles

• Alternate interior angles

Multiple Choice

Angle B and Angle R are...

• Alternate Interior Angles

• Consecutive Interior Angles

• Corresponding Angles

• Alternate Exterior Angles

Multiple Choice

Angle C and Angle P are...

• Alternate Interior Angles

• Consecutive Interior Angles

• Corresponding Angles

• Alternate Exterior Angles

Multiple Choice

Name the consecutive exterior interior angle to angle 1.

• 4

• 5

• 6

• 8

We can use the relationships of these angle pairs to find the measure of missing angles.

Multiple Choice

If the  $m\angle1\ =\ 57\degree,$  find the measure of  $\angle5$ ?

•  $123\degree$  

•  $57\degree$  

•  $180\degree$  

• Cannot be determined

Multiple Choice

Find y.

• 50

• 130

• 180

• 45

Multiple Choice

Find the value of x.

• x = 100

• x = 47

• x = 90

• x = 133

Multiple Choice

What is the measure of ∠6?

• 55

• 155

• 45

• 135

Multiple Choice

What is the measure of ∠1?

• 55

• 155

• 135

• 45

Multiple Choice

What is the measure of $\ \angle A$  ?

• 82°

• 98°

• 180°

• 8°

Sometimes we have to use our knowledge of solving equations to help us solve problems.

Just use the relationships between the angle pairs to write an equation, then solve.

Step 1: Identify the type of angle & relationship

These are consecutive interior angles. They are supplementary, so adding them together equals $180^o$  .

Step 2: Write the equation to solve.

Step 3: Solve the equation

Step 4: Check your answer

Don't forget that you can plug your answer back into the original figure/equation to check if it is correct.

Multiple Choice

Which is the correct equation to solve for x?

• $2x-10=4x+16$
  

• $\left(2x-10\right)+\left(4x+16\right)=180$
  

• $\left(2x-10\right)+\left(4x+16\right)=90$

Multiple Choice

Now, find the value of x.

• 13

• -3

• 29

• -13

Multiple Choice

Which of the following equations can be used to find the value of x?

• $\left(x+16\right)+\left(4x-5\right)=90$

• $x+16=4x-5$

• $\left(x+16\right)+\left(4x-5\right)=180$

Multiple Choice

Now solve for the value of x?

• 7

•  $3\ \frac{2}{3}$  
  

• 33.8

• 15.8

Multiple Choice

Which equation can be used to solve for x?

• $\left(3x\right)+\left(4x+19\right)=90$
  

• $\left(3x\right)+\left(4x+19\right)=180$

• $3x=4x+19$
  

Multiple Choice

What is the value of x?

• 22

• 26

• 24

• 23

Multiple Choice

Which is the correct equation to solve for x?

• $5x-8=3x+32$

• $\left(5x-8\right)+\left(3x+32\right)=90$

• $\left(5x-8\right)+\left(3x+32\right)=180$

Multiple Choice

Now, what is the value of x?

• 20

• 19.5

• 5

• 8.25